Complete question :
A study is conducted to assess the smoking behaviors of high-school seniors. A random sample of 8 seniors is selected and each student is asked the number of cigarettes consumed on a typical day. The (sorted) sample is: 0 0 3 4 5 8 10 18. If 18 is replaced with 20, then select all that apply:
Sample IQR will change
Range, IQR, and standard deviation will remain the same
Sample range will change.
Sample standard deviation will change
Answer:
Sample range will change
Sample Standard deviation will change
Explanation:
Given the sorted sample : 0,0,3, 4,5,8,10, 18
n = number of observations
Sample range : ( 18 - 0) = 10
Upper quartile (Q3) = 3/4(n+ 1) = 3/4(9) th term
Q3 = 27/4 = 6.75th term
(8 + 10) / 2 = 18/ 2 = 9
Lower quartile (Q1) = 1/4(n + 1) = 9/4 th term
2.25th term = 0+3 = 3/2 = 1.5
Interquartile range = 9 - 1.5 = 7.5
Standard deviation = 5.976 (using calculator)
If 18 is replaced by 20:
0,0,3, 4,5,8,10, 20
Range = (20 - 0). = 20
Upper quartile (Q3) = 3/4(n+ 1) = 3/4(9) th term
Q3 = 27/4 = 6.75th term
(8 + 10) / 2 = 18/ 2 = 9
Lower quartile (Q1) = 1/4(n + 1) = 9/4 th term
2.25th term = 0+3 = 3/2 = 1.5
Interquartile range = 9 - 1.5 = 7.5
Standard deviation = 6.563 (using calculator)